Unraveling the Art of Portfolio Selection: The Role of the Sharpe Ratio

In the world of investment, making informed choices is paramount. Building upon our previous article discussing the Coefficient of Variation (CV)
link : https://medium.com/@ayushmittal24/choosing-the-optimal-investment-portfolio-balancing-risk-and-return-9a788a48d9a6

and how it helped us identify the optimal portfolio, we now delve deeper into the intricacies of portfolio selection. It’s not just about risk and return, it’s also about incorporating the risk-free rate (Rf) into the equation.

The risk-free rate, represented by assets like Treasury bills and government bonds etc., offers guaranteed returns. With this rate in mind, how can investors determine the optimal portfolio?

To answer this question, we introduce a critical metric known as the Sharpe Ratio.
The Sharpe Ratio measures the incremental return over the risk-free rate per unit of risk taken. In simple terms, it gauges how much excess return you’ve earned for each unit of risk you’ve embraced.

Sharpe Ratio = (E(Rp) — Rf) / Risk
The underlying intuition is clear: when you invest in a portfolio, you’re willingly accepting a certain level of risk. Instead of investing in low-risk government securities and earning the risk-free rate, you’re investing into the portfolios in pursuit of higher returns. To justify this risk, you need a metric that quantifies the excess returns you’re aiming to achieve per unit of risk undertaken — that’s precisely what the Sharpe Ratio accomplishes.

Let’s revisit the two portfolios from our previous article:
Portfolio X: E(Rp) — 25%, Risk — 15%
Portfolio Y: E(Rp) — 15%, Risk — 10%
Assuming the risk-free rate (Rf) is 7%, we can now compute the Sharpe Ratios:
Sharpe Ratio for Portfolio A = (25% — 7%) / 15%
Sharpe Ratio for Portfolio B = (15% — 7%) / 10%

When evaluating these Sharpe Ratios, remember that higher values indicate a more favorable trade-off between risk and return. In this context, Portfolio X emerges as the superior choice, as it offers a higher Sharpe Ratio (1.2) as compared to portfolio Y (0.8), signifying that it provides greater excess return for each unit of risk assumed.

In conclusion, by considering the Sharpe Ratio, investors can make well-informed decisions, ensuring that their chosen portfolio is not only optimized for risk and return but also calibrated with respect to the risk-free rate. This strategic approach allows investors to maximize their returns while maintaining a balanced level of risk, aligning their investments with their financial objectives.